\newcommand{\nth}[1]{\frac{1}{#1}}
\newcommand{\nh}{\nth{\hbar}}


\newcommand{\myint}[4][dx]{\int^{#2}_{#3}{#4}\,{#1}}
\newcommand{\nint}[4][x]{\myint[d#1]{{#1}_{#2}}{{#1}_{#3}}{#4}}

\newcommand{\ket}[1]{\left|{#1}\right>}
\newcommand{\tket}[1]{$\left|{#1}\right>$}

\newcommand{\bra}[1]{\left<{#1}\right|}

\newcommand{\kup}{\left|{\uparrow}\right>}
\newcommand{\kdown}{\ket{\downarrow}}

\newcommand{\tkup}{$\ket{\uparrow}$}
\newcommand{\tkdown}{$\ket{\downarrow}$}

\newcommand{\br}[1]{\left({#1}\right)}
\newcommand{\mbr}[1]{\left[{#1}\right]}
\newcommand{\bbr}[1]{\left\{{#1}\right\}}
\newcommand{\abs}[1]{{\left|{{#1}}\right|}}

\newcommand{\op}[1]{\mathbf{#1}}

\newcommand{\tg}{\,\mbox{tg}\,}
\newcommand{\ctg}{\,\mbox{ctg}\,}


\newcommand{\dt}{\delta\theta}
\newcommand{\tet}{\theta}
\newcommand{\ho}{harmonic-oscillator}
\newcommand{\ep}{\epsilon}

\newcommand{\sx}{{\sigma_x}}
\newcommand{\sy}{{\sigma_y}}
\newcommand{\sz}{{\sigma_z}}

\newcommand{\ld}{\lambda}

\newcommand{\vk}{{\mathbf{k}}}
\newcommand{\vkp}{{\mathbf{k'}}}
\newcommand{\vq}{{\mathbf{q}}}
\newcommand{\vqt}{{\frac{\mathbf{q}}{2}}}
\providecommand{\ol}[1]{\overline{#1}}


\newcommand{\kp}{\ket{\Psi}}
\newcommand{\kpp}{\ket{\Psi_P}}
\newcommand{\kpq}{\ket{\Psi_Q}}


\newcommand{\pse}{{\psi_{E'}}}

\newcommand{\asym}{\stackrel{r->\infty}{\longrightarrow}}

\newcommand{\md}{ many\_body}
\newcommand{\td}{ two\_body}

\newcommand {\dc}{\delta_c}

\newcommand {\der}[2]{{\frac{{\partial}#1}{{\partial}#2}}}

\newcommand {\Fok}{F^o_\vk}
\newcommand {\Fck}{F^c_\vk}

\newcommand {\pok}{\psi^0_\vk}

\newcommand {\teta}{\tilde{\eta}}

\newcommand{\as}{{$\textbf{a}_s$}}
